Vetinari's luxury dungeon cell blows the mind every time one reads about it.
Not just the cell itself, the rats. Dear god, the rats.
Carrot arresting a dragon.
For its own protection.
At the conclusion, when told to throw the book at Lupine Wonse, he obliges. As it happened, the aforementioned book weighed several pounds, and caused the head clerk to tumble backwards, and fall several stories to his death.
Another, earlier one, besides beating an entire bar, including a bunch of trolls, is when he was told to 'charge these men', meaning arrest them. He promptly backs away, and the reader has enough time to remember he takes everything literally... when Carrot runs, screaming, at the men, two axes in each hand, throws the axes, barely missing, and then runs at the armed men bare-handed. This is only the establishing moment of awesome, however.
We get an early evidence of Carrot's charisma when his speech to an entire bar's worth of drunken and fighty dwarves cause them all to realise the error of their ways, weep in shame and decide to write back home to their mums.
Remember the reasons for this, one explicit and one only alluded to. He IS culturally, if not literally, a dwarf himself, and he is... possibly... the actual king of Ankh-Morpork.
Pratchett is fond of characters paraphrasing the "Do you feel lucky?" speech from Dirty Harry. It gives Vimes one of his earliest awesome moments, in Guards! Guards!.
Guards! Guards! has FABRICATI DIEM, PVNC engraved over the door of the Watch House, for more Dirty Harry-based fun.
Although the Dragon was a villain (sort-of), the Dragon becoming King (or rather, Queen) of Ankh-Morpork.
Vetinari's speech to Vimes about the nature of men's souls and the sea of evil is a character-establishing moment for Vetinari.
Vetinari: "A person like you thinks that there are good men and bad men... There are, always and only, bad men - but some of them are on different sides."
And Vimes' response is one for him.
Better yet, Colon's and Nobby's unknown refutation of the whole idea, when they innocently ask for nothing more than a tiny raise and a new teapot as a reward for saving the entire city. Moreso, in that they're not black-and-white thinkers like Vimes, but just a couple of regular, flawed schlubs who couldn't be actual villains if they tried.
Carrot, Colon, and Nobby try to shoot the dragon in the vulnerables. Granted, it utterly fails, but given how many close scrapes they've had already, and how obviously reluctant Colon and Nobby are, it's impressive they still had the bottle to try. Not to mention they had a pretty decent graspof how the Discworld works.
The swamp dragon Errol when he finally gets done rearranging his digestive tract. The dragon kennels exploded. The windows blew out. The door left the wall ahead of a great billow of black smoke and sailed into the air, tumbling slowly, to plow into the rhododendrons... Now Errol’s flame was visible, so hot as to be almost blue. The landscape rolled away underneath him at an impossible speed, and he was accelerating.
In short, Errol invents the jet engine.
Sybil. You've got to admire a woman who happily works with creatures which have, at this point, burned off all her hair, and could, at any moment, explode. Similarly, her reaction to the giant dragon attacking the city isn't to run scared, but to want to get a good view of it.
Also, the totally practical way she handles a wounded Vimes.
Not to mention that when guards come to take her away to be a Virgin Sacrifice she attacks them with a battle axe.